Despite some high-level similarities to other approaches, our framework is unusual in approximating the posterior by a sampled mixture of variational approximations. The Mixture Kalman filter [1]} is a special case of this, which uses a sampled mixture of Gaussians, each constructed as a Kalman filter. A related approach is to optimize a parameterized function that generates mixture components [2]}, [3]}, and generative diffusion models can also be seen as a case of this approach [4]}, [5]}. Our work differs in that we derived a closed-form mixing distribution that requires no additional learning or optimization.
